Duh. Glanced at the first line of Peachey's answer and didn't read the rest. My apologies. I wish italki let us edit these answers.

I agree with the other members - and you don't have to be American to hear it either. It's clear to any native speaker than the priest has a non-native accent. What's more, anyone who has a good ear for accents can tell that he's a Russian speaker : it's the typically Russian 'L' sound which is the give-away.

He speaks with a slight accent.

He has a very clear and well-spoken accent, but with both US and UK influences (the UK influences turn up in a couple of vowel sounds). Why did we all assume he was Russian? He was born in the US and has spent a lot of time in the UK. :) (I mean, I don't doubt he speaks Russian, but some of us have jumped the gun here.) http://orthodoxwiki.org/Irenaeus_(Steenberg) I'm actually reminded of the accent that Christoph Waltz used for his Dr Schultz character in Django Unchained. It's a careful, measured and practised accent.

The narrator has a very very good American accent. However, there is an obvious slight Russian accent that any American would detect.